ABJM matrix model and 2D Toda lattice hierarchy

  • Tomohiro Furukawa
  • Sanefumi MoriyamaEmail author
Open Access
Regular Article - Theoretical Physics


It was known that one-point functions in the ABJM matrix model (obtained by applying the localization technique to one-point functions of the half-BPS Wilson loop operator in the ABJM theory) satisfy the Jacobi-Trudi formula, which strongly indicates the integrable structure of the system. In this paper, we identify the integrable structure of two-point functions in the ABJM matrix model as the two-dimensional Toda lattice hierarchy. The identification implies infinitely many non-linear differential equations for the generating function of the two-point functions.


Chern-Simons Theories Integrable Hierarchies M-Theory Matrix Models 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Physics, Graduate School of ScienceOsaka City UniversityOsakaJapan
  2. 2.Osaka City University Advanced Mathematical Institute (OCAMI)OsakaJapan
  3. 3.Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP)OsakaJapan

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